DISCOVERING THE UNIVERSE FOR YOURSELF -...

D I S C O V E R I N G T H E U N I V E R S E F O R Y O U R S E L F

DISCOVERING THE UNIVERSE FOR YOURSELF

LEARNING GOALS

3 THE MOON, OUR CONSTANT COMPANION

■ Why do we see phases of the Moon?■ What causes eclipses?

4 THE ANCIENT MYSTERY OF THE PLANETS

■ Why was planetary motion so hard to explain?■ Why did the ancient Greeks reject the real explanation

for planetary motion?

1 PATTERNS IN THE NIGHT SKY

■ What does the universe look like from Earth?■ Why do stars rise and set?■ Why do the constellations we see depend on latitude

and time of year?

2 THE REASON FOR SEASONS

■ What causes the seasons?■ How does the orientation of Earth’s axis change

with time?

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We had the sky, up there, all speckled with stars, and we used to lay on our backs and look up at them, and discuss about whether they was made, or only just happened.

—Mark Twain, Huckleberry Finn

This is an exciting time in the history of astronomy. A new generation of telescopes is scanning the depths of the

universe. Increasingly sophisticated space probes are collecting new data about the planets and other objects in our solar system. Rapid advances in computing technology are allowing scien-tists to analyze the vast amount of new data and to model the processes that occur in planets, stars, galaxies, and the universe.

One goal of this book is to help you share in the ongoing adventure of astronomical discovery. One of the best ways to become a part of this adventure is to do what other humans have done for thousands of generations: Go outside, observe the sky around you, and contemplate the awe-inspiring universe of which you are a part. In this chapter, we’ll discuss a few key ideas that will help you understand what you see in the sky.

1 PATTERNS IN THE NIGHT SKY

Today we take for granted that we live on a small planet orbit-ing an ordinary star in one of many galaxies in the universe. But this fact is not obvious from a casual glance at the night sky, and we’ve learned about our place in the cosmos only through a long history of careful observations. In this section, we’ll discuss major features of the night sky and how we understand them in light of our current knowledge of the universe.

What does the universe look like from Earth?

Shortly after sunset, as daylight fades to darkness, the sky appears to slowly fill with stars. On clear, moonless nights far from city lights, more than 2000 stars may be visible to your naked eye, along with the whitish band of light that we call the Milky Way (FIGURE 1). As you look at the stars, your mind may group them into patterns that look like familiar shapes or objects. If you observe the sky night after night or year after year, you will recognize the same patterns of stars. These patterns have not changed noticeably in the past few thousand years.

Constellations People of nearly every culture gave names to patterns they saw in the sky. We usually refer to such patterns as constellations, but to astronomers the term has a more precise meaning: A constellation is a region of the sky with well-defined borders; the familiar patterns of stars merely help us locate the constellations. Just as every spot of land in the continental United States is part of some state, every point in the sky belongs to some constellation. FIGURE 2 shows the borders of the constellation Orion and several of its neighbors.

FIGURE 1 This photo shows the Milky Way over Haleakala crater on the island of Maui, Hawaii. The bright spot just below (and slightly left of) the center of the band is the planet Jupiter.

The names and borders of the 88 official constella-tions were chosen in 1928 by members of the International Astronomical Union (IAU). Most of the IAU members lived in Europe or the United States, so they chose names famil-iar in the western world. That is why the official names for constellations visible in the Northern Hemisphere can be traced back to civilizations of the ancient Middle East,

Orion

Lepus

Canis Minor

Monoceros

Procyon Betelgeuse

Rigel

Sirius

Canis Major

Winter Triangle

FIGURE 2 Red lines mark official borders of several constellations near Orion. Yellow lines connect recognizable patterns of stars within constellations. Sirius, Procyon, and Betelgeuse form a pattern that spans several constellations and is called the Winter Triangle. This view shows how it appears on winter evenings from the Northern Hemisphere.

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■ The ecliptic is the path the Sun follows as it appears to circle around the celestial sphere once each year. It crosses the celestial equator at a 231

2° angle, because that is the tilt of Earth’s axis.

The Milky Way The band of light that we call the Milky Way circles all the way around the celestial sphere, passing through more than a dozen constellations. The widest and brightest parts of the Milky Way are most easily seen from the Southern Hemisphere, which probably explains why the Aborigines of Australia gave names to patterns within the Milky Way in the same way other cultures named patterns of stars.

Our Milky Way Galaxy gets its name from this band of light, and the two “Milky Ways” are closely related: The Milky Way in the night sky traces our galaxy’s disk of stars—the galactic plane—as it appears from our location within the Milky Way Galaxy. FIGURE 5 shows the idea. Our galaxy is shaped like a thin pancake with a bulge in the middle. We view the universe from our location a little more than half-way out from the center of this “pancake.” In all directions that we look within the pancake, we see the countless stars and vast interstellar clouds that make up the Milky Way in the night sky; that is why the band of light makes a full circle around our sky. The Milky Way appears somewhat wider in the direction of the constellation Sagittarius, because that is the direction in which we are looking toward the galaxy’s central bulge. We have a clear view to the distant universe only when we look away from the galactic plane, along directions that have relatively few stars and clouds to block our view.

The dark lanes that run down the center of the Milky Way contain the densest clouds, obscuring our view of stars behind them. In fact, these clouds generally prevent us from seeing more than a few thousand light-years into our galaxy’s disk. As a result, much of our own galaxy remained hidden from view until just a few decades ago, when new techno logies allowed us to peer through the clouds by observing forms of light that are invisible to our eyes (such as radio waves and X rays).

while Southern Hemisphere constellations carry names that originated with 17th-century European explorers.

Recognizing the patterns of just 20 or so constellations is enough to make the sky seem as familiar as your own neighbor-hood. The best way to learn the constellations is to go out and view them, guided by a few visits to a planetarium, star charts, or sky-viewing apps for smart phones and tablets.

The Celestial Sphere The stars in a particular constel-lation appear to lie close to one another but may be quite far apart in reality, because they may lie at very different distances from Earth. This illusion occurs because we lack depth perception when we look into space, a consequence of the fact that the stars are so far away. The ancient Greeks mistook this illusion for reality, imagining the stars and con-stellations to lie on a great celestial sphere that surrounds Earth (FIGURE 3).

We now know that Earth seems to be in the center of the celestial sphere only because it is where we are located as we look into space. Nevertheless, the celestial sphere is a useful illusion, because it allows us to map the sky as seen from Earth. For reference, we identify four special points and circles on the celestial sphere (FIGURE 4).

■ The north celestial pole is the point directly over Earth’s North Pole.

■ The south celestial pole is the point directly over Earth’s South Pole.

■ The celestial equator, which is a projection of Earth’s equator into space, makes a complete circle around the celestial sphere.

FIGURE 3 The stars and constellations appear to lie on a celestial sphere that surrounds Earth. This is an illusion created by our lack of depth perception in space, but it is useful for mapping the sky.

northcelestial

pole

southcelestial

pole

Stars all appear tolie on the celestialsphere, but really lieat different distances.

Cetus

Phoenix

FornaxSculptor

Eridan

us

Cassiopeia

Milky Way

Taur

us

Aries

Perseus Andromeda

Pegasus

Pisc

es

Aquarius

ecliptic

celestial equator

12

north celestial pole

south celestial pole

celestial equator

23 �ecliptic

The north celestialpole is directly aboveEarth's North Pole. The ecliptic is

the Sun's apparentannual path aroundthe celestial sphere.

The south celestial poleis directly above Earth'sSouth Pole.

The celestial equatoris a projection ofEarth's equator intospace.

FIGURE 4 This schematic diagram shows key features of the celestial sphere.

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M AT H E M AT I CA L I N S I G H T 1Angular Size, Physical Size, and Distance

An object’s angular size depends on its physical (actual) size and distance. FIGURE 1a shows the basic idea: An object’s physical size does not change as you move it farther from your eye, but its angular size gets smaller, making it appear smaller against the background.

FIGURE 1b shows a simple approximation that we can use to find a formula relating angular size to physical size and distance. As long as an object’s angular size is relatively small (less than a few degrees), its physical size (diameter) is similar to that of a small piece of a circle going all the way around your eye with a radius equal to the object’s distance from your eye. The object’s angular size (in degrees) is there-fore the same fraction of the full 360° circle as its physical size is of the circle’s full circumference (given by the formula 2p * distance). That is,

angular size360°

=physical size

2p * distance

We solve for the angular size by multiplying both sides by 360°:

angular size = physical size *360°

2p * distance

This formula is often called the small-angle formula, because it is valid only when the angular size is small.

EXAMPLE 1 : The two headlights on a car are separated by 1.5 meters. What is their angular separation when the car is 500 meters away?

SOLUTION:

Step 1 Understand: We can use the small-angle formula by thinking of the “separation” between the two lights as a “size.” That is, if we set the physical size to the actual separation of 1.5 meters, the small-angle formula will tell us the angular separation.

Step 2 Solve: We simply plug in the given values and solve:

angular separation

= physical separation *360°

2p * distance

= 1.5 m *360°

2p * 500 m≈ 0.17°

Step 3 Explain: We have found that the angular separation of the two headlights is 0.17°. This small angle will be easier to interpret if we convert it to arcminutes. There are 60 arcminutes in 1°, so 0.17°is equivalent to 0.17 * 60 = 10.2 arcminutes. In other words, the

angular separation of the headlights is about 10 arcminutes, or about a third of the 30 arcminute (0.5°) angular diameter of the Moon.

EXAMPLE 2 : Estimate the Moon’s actual diameter from its angular diameter of about 0.5° and its distance of about 380,000 km.

SOLUTION:

Step 1 Understand: We are seeking to find a physical size (diam-eter) from an angular size and distance. We therefore need to solve the small-angle formula for the physical size, which we do by switching its left and right sides and multiplying both sides by (2p * distance)/360°:

physical size = angular size *2p * distance

360°

Step 2 Solve: We now plug in the given values of the Moon’s angular size and distance:

physical size = 0.5° *2p * 380,000 km

360°≈ 3300 km

Step 3 Explain: We have used the Moon’s approximate angular size and distance to find that its diameter is about 3300 kilometers. We could find a more exact value (3476 km) by using more precise values for the angular diameter and distance.

distance

angularsize

physicalsize

a

b

The angular size of this object . . .

. . . becomes smalleras the object moves farther away.

As long as the angular size issmall, we can think of theobject’s physical sizeas a small piece of a circle.

FIGURE 1 Angular size depends on physical size and distance.

size also depends on distance. The Sun is about 400 times as large in diameter as the Moon, but it has the same angular size in our sky because it is also about 400 times as far away.

The angular distance between a pair of objects in the sky is the angle that appears to separate them. For example, the angular distance between the “pointer stars” at the end of the Big Dipper’s bowl is about 5° and the angular length of the Southern Cross is about 6° (FIGURE 7b). You can use your

outstretched hand to make rough estimates of angles in the sky (FIGURE 7c).

For more precise astronomical measurements, we subdi-vide each degree into 60 arcminutes and subdivide each arcminute into 60 arcseconds (FIGURE 8). We abbreviate arcminutes with the symbol ′ and arcseconds with the symbol ″. For example, we read 35°27′15″ as “35 degrees, 27 arcminutes, 15 arcseconds.”

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FIGURE 6 shows key reference features of the local sky. The boundary between Earth and sky defines the horizon. The point directly overhead is the zenith. The meridian is an imaginary half circle stretching from the horizon due south, through the zenith, to the horizon due north.

We can pinpoint the position of any object in the local sky by stating its direction along the horizon (sometimes stated as azimuth, which is degrees clockwise from due north) and its altitude above the horizon. For example, Figure 6 shows a person pointing to a star located in the direction of southeast at an altitude of 60°. Note that the zenith has altitude 90° but no direction, because it is straight overhead.

Angular Sizes and Distances Our lack of depth per-ception on the celestial sphere means we have no way to judge the true sizes or separations of the objects we see in the sky. However, we can describe the angular sizes or separations of objects without knowing how far away they are.

The angular size of an object is the angle it appears to span in your field of view. For example, the angular sizes of the Sun and Moon are each about 12° (FIGURE 7a). Note that angular size does not by itself tell us an object’s true size, because angular

When we look out of the galactic plane (white arrows),we have a clear view to the distant universe.

Galactic plane

Location of oursolar system

When we lookin any direction

into the galactic plane(blue arrows),we see the

stars and interstellar clouds thatmake up the Milky Way in the night sky.

FIGURE 5 This painting shows how our galaxy’s structure affects our view from Earth.

T H I N K A B O U T I TConsider a distant galaxy located in the same direction from Earth as the center of our own galaxy (but much farther away). Could we see it with our eyes? Explain.

zenith(altitude = 90°)

meridian

E60°

SW

altitude = 60°direction = SE

N

horizon(altitude = 0°)

FIGURE 6 From any place on Earth, the local sky looks like a dome (hemisphere). This diagram shows key reference points in the local sky. It also shows how we can describe any position in the local sky by its altitude and direction.

a The angular sizes of the Sun and the Moon are about 1/2�.

b The angular distance between the "pointer stars" of the Big Dipper is about 5�, and the angular length of the Southern Cross is about 6°.

c You can estimate angular sizes or distances with your outstretched hand.

12

Moon Big Dipper

5�

6�10�

20�1�

Stretch out your arm as shown here.

�

SouthernCross

to Polaris

FIGURE 7 We measure angular sizes or angular distances, rather than actual sizes or distances, when we look at objects in the sky.

The Local Sky The celestial sphere provides a useful way of thinking about the appearance of the universe from Earth. But it is not what we actually see when we go outside. Instead, your local sky—the sky as seen from wherever you happen to be standing—appears to take the shape of a hemisphere or dome, which explains why people of many ancient cultures imagined that we lived on a flat Earth under a great dome encompassing the world. The dome shape arises from the fact that we see only half of the celestial sphere at any particu-lar moment from any particular location, while the ground blocks the other half from view.

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Why do stars rise and set?

If you spend a few hours out under a starry sky, you’ll notice that the universe seems to be circling around us, with stars moving gradually across the sky from east to west. Many ancient people took this appearance at face value, concluding that we lie at the center of a universe that rotates around us each day. Today we know that the ancients had it backward: It is Earth that rotates daily, not the rest of the universe.

We can picture the movement of the sky by imagining the celestial sphere rotating around Earth (FIGURE 9). From this perspective you can see how the universe seems to turn around us: Every object on the celestial sphere appears to make a simple daily circle around Earth. However, the motion can look a little more complex in the local sky, because the horizon cuts the celestial sphere in half. FIGURE 10 shows the idea for a location in the United States. If you study the figure carefully,

0�

1�

10�

20�

30�

40�

50�

60�

0�

10�

20�

30�

40�

50�

60�

60�

1� 60�

Not to scale!

1� �

�

FIGURE 8 We subdivide each degree into 60 arcminutes and each arcminute into 60 arcseconds.

T H I N K A B O U T I TChildren often try to describe the sizes of objects in the sky (such as the Moon or an airplane) in inches or miles, or by hold-ing their fingers apart and saying “it was THIS big.” Can we really describe objects in the sky in this way? Why or why not?

The Moon Illusion

You’ve probably noticed that the full moon appears to be larger when it is near the horizon than when it is high in

your sky. However, this apparent size change is an illusion: If you compare the Moon’s angular size to that of a small object (such as a small button) held at arm’s length, you’ll see that it remains essentially the same throughout the night. The reason is that the Moon’s angular size depends on its true size and distance, and while the latter varies over the course of the Moon’s monthly orbit, it does not change enough to cause a noticeable effect on a single night. The Moon illusion clearly occurs within the human brain, though its precise cause is still hotly debated. Interestingly, you may be able to make the illusion go away by viewing the Moon upside down between your legs.

C O M M O N M I S C O N C E P T I O N S



celestial equator

FIGURE 9 Earth rotates from west to east (black arrow), making the celestial sphere appear to rotate around us from east to west (red arrows).

you’ll notice the following key facts about the paths of various stars through the local sky:

■ Stars near the north celestial pole are circumpolar, mean-ing that they remain perpetually above the horizon, circling (counterclockwise) around the north celestial pole each day.

■ Stars near the south celestial pole never rise above the horizon at all.

■ All other stars have daily circles that are partly above the horizon and partly below it, which means they appear to rise in the east and set in the west.

The time-exposure photograph that opens this chap-ter, taken at Arches National Park in Utah, shows a part of the daily paths of stars. Paths of circumpolar stars are visi-ble within the arch; notice that the complete daily circles for these stars are above the horizon, although the photo shows only a portion of each circle. The north celestial pole lies at the center of these circles. The circles grow larger for stars farther



zenith

celestial equator

This star iscircumpolar.

Its daily circle isentirely above

your horizon.

This star isnever seen.

Other stars rise inthe east and setin the west.

FIGURE 10 The local sky for a location in the United States (40°N). The horizon slices through the celestial sphere at an angle to the equa-tor, causing the daily circles of stars to appear tilted in the local sky. Note: It may be easier to follow the star paths in the local sky if you rotate the page so that the zenith points up.

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constellations than you see at home. And even if you stay in one place, you’ll see different constellations at different times of year. Let’s explore why.

Variation with Latitude Latitude measures north-south position on Earth, and longitude measures east-west position (FIGURE 11). Latitude is defined to be 0° at the equa-tor, increasing to 90°N at the North Pole and 90°S at the South Pole. By international treaty, longitude is defined to be 0°along the prime meridian, which passes through Greenwich, England. Stating a latitude and a longitude pinpoints a loca-tion on Earth. For example, Miami lies at about 26°N latitude and 80°W longitude.

Latitude affects the constellations we see because it affects the locations of the horizon and zenith relative to the celestial sphere. FIGURE 12 shows how this works for the latitudes of the North Pole (90°N) and Sydney, Australia (34°S). Note that although the sky varies with latitude, it does not vary with longi-tude. For example, Charleston (South Carolina) and San Diego (California) are at about the same latitude, so people in both cities see the same set of constellations at night.

You can learn more about how the sky varies with latitude by studying diagrams like those in Figures 10 and 12. For example, at the North Pole, you can see only objects that lie on the north-ern half of the celestial sphere, and they are all circumpolar. That is why the Sun remains above the horizon for 6 months at the North Pole: The Sun lies north of the celestial equator for half of each year (see Figure 3), so during these 6 months it circles the sky at the North Pole just like a circumpolar star.

The diagrams also show a fact that is very important to navigation:

The altitude of the celestial pole in your sky is equal toyour latitude.

Greenwich

Miami:latitude = 26�N

longitude = 80�W

Latitude is measurednorth or south of theequator.

The prime meridian (longitude = 0°) passes through Greenwich, England.

Longitude is measuredeast or west of theprime meridian.

a We can locate any place on Earth‘s surface by its latitude and longitude.

b The entrance to the Old Royal Greenwich Observatory, near London. The line emerging from the door marks the prime meridian.

equator

long. = 30 � W

long. = 60 � W

lat. = 60

� N

lat. = 0�

lat. = 30� N

long. = 0 �

lat. = 60� S lat. = 30

� S

long. = 90 � W

long. = 120 � W

FIGURE 11 Definitions of latitude and longitude.

Stars in the Daytime

Stars may appear to vanish in the daytime and “come out” at night, but in reality the stars are always present.

The reason you don’t see stars in the daytime is that their dim light is overwhelmed by the bright daytime sky. You can see bright stars in the daytime with the aid of a telescope, or if you are fortunate enough to observe a total eclipse of the Sun. Astronauts can also see stars in the daytime. Above Earth’s atmosphere, where there is no air to scatter sunlight, the Sun is a bright disk against a dark sky filled with stars. (However, the Sun is so bright that astronauts must block its light if they wish to see the stars.)


T H I N K A B O U T I TDo distant galaxies also rise and set like the stars in our sky? Why or why not?

from the north celestial pole. If they are large enough, the circles cross the horizon, so that the stars rise in the east and set in the west. The same ideas apply in the Southern Hemisphere, except that circumpolar stars are those near the south celestial pole and they circle clockwise rather than counter-clockwise.

Why do the constellations we see depend on latitude and time of year?

If you stay in one place, the basic patterns of motion in the sky will stay the same from one night to the next. However, if you travel far north or south, you’ll see a different set of

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For example, if you see the north celestial pole at an alti-tude of 40° above your north horizon, your latitude is 40°N. Similarly, if you see the south celestial pole at an altitude of 34° above your south horizon, your latitude is 34°S. You can therefore determine your latitude simply by finding the celes-tial pole in your sky (FIGURE 13). Finding the north celestial pole is fairly easy, because it lies very close to the star Polaris, also known as the North Star (Figure 13a). In the Southern



34�

34�

“up”(zenith)

celestial equator



celestial equator

90�

90�

a� The local sky at the North Pole (latitude 90�N).

“up” (zenith)

b��The local sky at latitude 34�S.

FIGURE 12 The sky varies with latitude. Notice that the altitude of the celestial pole that is visible in your sky is always equal to your latitude.

Hemisphere, you can find the south celestial pole with the aid of the Southern Cross (Figure 13b).

a The pointer stars of the Big Dipper point to the North Star, Polaris, which lies within 1� of the north celestial pole. The sky appears to turn counterclockwise around the north celestial pole.

b The Southern Cross points to the south celestial pole, which is not marked by any bright star. The sky appears to turn clockwise around the south celestial pole.

looking northward in the Northern Hemisphere looking southward in the Southern Hemisphere

position after2 hours



Polaris

Little DipperBig Dipper

pointer stars


SouthernCross




about 4cross lengths

FIGURE 13 You can determine your latitude by measuring the altitude of the celestial pole in your sky.

S E E I T F O R YO U R S E L FWhat is your latitude? Use Figure 13 to find the celestial pole in your sky, and estimate its altitude with your hand as shown in Figure 7c. Is its altitude what you expect?

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Follow the “Night” arrow for Aug, 21: Noticethat Aquarius is opposite the Sun in the sky,and hence visible all night long.

Follow the “Day” arrow forAug. 21: Notice that the Sunappears to be in Leo.

Day

Night

Taurus

Pisces

Capricornus

Sagittarius

AquariusAries

Gemini

LeoVirgo

Libra

Scorpius

Ophiuchus

Earth’s actual position in orbit

the Sun’s apparent position in the zodiac

July 21

June 21

May 21

Apr. 21Mar. 21

Jan. 21

Dec. 21

Oct. 21

Cancer

Sept. 21

Feb. 21

Nov. 21

Sept. 21

Aug. 21

July 21

June 21

May 21

Apr. 21Feb. 21

Jan. 21

Dec.21

Oct. 21

Nov. 21

Mar. 21

Aug. 21

FIGURE 14 The Sun appears to move steadily eastward along the ecliptic as Earth orbits the Sun, so we see the Sun against the background of different zodiac constellations at differ-ent times of year. For example, on August 21 the Sun appears to be in Leo, because it is between us and the much more distant stars that make up Leo.

Seasons Tutorial, Lessons 1–3

2 THE REASON FOR SEASONS

We have seen how Earth’s rotation makes the sky appear to circle us daily and how the night sky changes as Earth orbits the Sun each year. The combination of Earth’s rotation and orbit also leads to the progression of the seasons.

What causes the seasons?

You know that we have seasonal changes, such as longer and warmer days in summer and shorter and cooler days in winter. But why do the seasons occur? The answer is that the tilt of Earth’s axis causes sunlight to fall differently on Earth at different times of year.

FIGURE 15 illustrates the key ideas. Step 1 illustrates the tilt of Earth’s axis, which remains pointed in the same direction in space (toward Polaris) throughout the year. As a result, the

Variation with Time of Year The night sky changes throughout the year because of Earth’s changing position in its orbit around the Sun. FIGURE 14 shows how this works. As Earth orbits, the Sun appears to move steadily eastward along the ecliptic, with the stars of different constellations in the background at different times of year. The constellations along the ecliptic make up what we call the zodiac; tradition places 12 constellations along the zodiac, but the official bor-ders include a thirteenth constellation, Ophiuchus.

The Sun’s apparent location along the ecliptic determines which constellations we see at night. For example, Figure 14 shows that the Sun appears to be in Leo in late August. We there-fore cannot see Leo at this time (because it is in our daytime sky), but we can see Aquarius all night long because of its location opposite Leo on the celestial sphere. Six months later, in February, we see Leo at night while Aquarius is above the horizon only in the daytime.

What Makes the North Star Special?

Most people are aware that the North Star, Polaris, is a special star. Contrary to a relatively common belief,

however, it is not the brightest star in the sky. More than 50 other stars are just as bright or brighter. Polaris is special not because of its brightness, but because it is so close to the north celestial pole and therefore very useful in navigation.


S E E I T F O R YO U R S E L FBased on Figure 14 and today’s date, in what constellation does the Sun currently appear? What constellation of the zodiac will be on your meridian at midnight? What constellation of the zodiac will you see in the west shortly after sunset? Go outside at night to confirm your answers to the last two questions.

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Solstices and Equinoxes To help us mark the chang-ing seasons, we define four special moments in the year, each of which corresponds to one of the four special positions in Earth’s orbit shown in Figure 15.

■ The summer (June) solstice, which occurs around June 21, is the moment when the Northern Hemisphere is tipped most directly toward the Sun and receives the most direct sunlight.

■ The winter (December) solstice, which occurs around December 21, is the moment when the Northern Hemi-sphere receives the least direct sunlight.

■ The spring (March) equinox, which occurs around March 21, is the moment when the Northern Hemisphere goes from being tipped slightly away from the Sun to being tipped slightly toward the Sun.

■ The fall (September) equinox, which occurs around September 22, is the moment when the Northern Hemi-sphere first starts to be tipped away from the Sun.

The exact dates and times of the solstices and equi-noxes vary from year to year, but stay within a couple of days of the dates given above. In fact, our modern calen-dar includes leap years in a pattern specifically designed to keep the solstices and equinoxes around the same dates.

We can mark the dates of the equinoxes and solstices by observing changes in the Sun’s path through our sky (FIGURE 16). The equinoxes occur on the only two days of the year on which the Sun rises precisely due east and sets precisely due west. The June solstice occurs on the day on which the Sun follows its longest and highest path through the Northern Hemisphere sky (and its shortest and lowest path through the Southern Hemisphere sky). It is therefore the day on which the Sun rises and sets farther to the north than on any other day of the year, and on which the noon Sun reaches its highest point in the Northern Hemisphere sky. The opposite is true on the day of the December solstice, when the Sun rises and sets farthest to the south and the noon Sun is lower in the Northern Hemisphere sky than on any other day of the year. FIGURE 17 shows how the Sun’s position in the sky varies over the course of the year.

First Days of Seasons We usually say that each equi-nox and solstice marks the first day of a season. For example, the day of the summer solstice is usually called the “first day of summer.” Notice, however, that the summer (June) solstice occurs when the Northern Hemisphere has its maximum tilt toward the Sun. You might then wonder why we consider the solstice to be the beginning rather than the midpoint of summer.

The choice is somewhat arbitrary, but it makes sense in at least two ways. First, it was much easier for ancient people to identify the days on which the Sun reached extreme positions in the sky—such as when it reached its highest point on the summer solstice—than other days in between.

orientation of the axis relative to the Sun changes over the course of each orbit: The Northern Hemisphere is tipped toward the Sun in June and away from the Sun in December, while the reverse is true for the Southern Hemisphere. That is why the two hemispheres experience opposite seasons. The rest of the figure shows how the changing angle of sunlight on the two hemi-spheres leads directly to seasons.

Step 2 shows Earth in June, when axis tilt causes sunlight to strike the Northern Hemisphere at a steeper angle and the Southern Hemisphere at a shallower angle. The steeper sunlight angle makes it summer in the Northern Hemisphere for two reasons. First, as shown in the zoom-out, the steeper angle means more concentrated sunlight, which tends to make it warmer. Second, if you visualize what happens as Earth rotates each day, you’ll see that the steeper angle also means the Sun follows a longer and higher path through the sky, giving the Northern Hemisphere more hours of daylight during which it is warmed by the Sun. The opposite is true for the Southern Hemisphere at this time: The shallower sunlight angle makes it winter there because sunlight is less concen-trated and the Sun follows a shorter, lower path through the sky.

The sunlight angle gradually changes as Earth orbits the Sun. At the opposite side of Earth’s orbit, Step 4 shows that it has become winter for the Northern Hemisphere and summer for the Southern Hemisphere. In between these two extremes, Step 3 shows that both hemispheres are illuminated equally in March and September. It is therefore spring for the hemisphere that is on the way from winter to summer, and fall for the hemisphere on the way from summer to winter.

Notice that the seasons on Earth are caused only by the axis tilt and not by any change in Earth’s distance from the Sun. Although Earth’s orbital distance varies over the course of each year, the variation is fairly small: Earth is only about 3% farther from the Sun at its farthest point than at its nearest. The difference in the strength of sunlight due to this small change in distance is easily overwhelmed by the effects caused by the axis tilt. If Earth did not have an axis tilt, we would not have seasons.

T H I N K A B O U T I TJupiter has an axis tilt of about 3°, small enough to be insignifi-cant. Saturn has an axis tilt of about 27°, slightly greater than that of Earth. Both planets have nearly circular orbits around the Sun. Do you expect Jupiter to have seasons? Do you expect Saturn to have seasons? Explain.

The Cause of Seasons

Many people guess that seasons are caused by variations in Earth’s distance from the Sun. But if this were true, the

whole Earth would have summer or winter at the same time, and it doesn’t: The seasons are opposite in the Northern and Southern Hemispheres. In fact, Earth’s slightly varying orbital distance has virtually no effect on the weather. The real cause of the seasons is Earth’s axis tilt, which causes the two hemispheres to take turns being tipped toward the Sun over the course of each year.


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N23½°

Earth’s seasons are caused by the tilt of its rotation axis, which is why the seasons are opposite in the two hemispheres. The seasons do not depend on Earth’s distance from the Sun, which varies only slightly throughout the year.

Axis Tilt: Earth’s axis points in the same direction throughout the year, which causes changes in Earth’s orientation relative to the Sun.

Northern Summer/Southern Winter: In June, sunlight falls more directly on the Northern Hemisphere, which makes it summer there because solar energy is more concentrated and the Sun follows a longer and higher path through the sky. The Southern Hemisphere receives less direct sunlight, making it winter.

Summer (June) Solstice

The Northern Hemisphere is tipped most directly toward the Sun.

1 2

S

152.1 million km147.1 million km

July 4

Fall Equinox

Spring Equinox

January 3

Noon rays of sunlight hit the ground at a steeper angle in the Northern Hemisphere, meaning more concentrated sunlight and shorter shadows.

Noon rays of sunlight hit the ground at a shallower angle in the Southern Hemisphere, meaning less concentrated sunlight and longer shadows.

Interpreting the Diagram

To interpret the seasons diagram properly, keep in mind:

1. Earth's size relative to its orbit would be microscopic on this scale, meaning that both hemispheres are at essentially the same distance from the Sun.

2. The diagram is a side view of Earth's orbit. A top-down view (below) shows that Earth orbits in a nearly perfect circle and comes closest to the Sun in January.

C O S M I C C O N T E X T F I G U R E 15 The Seasons

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Spring (March) Equinox

The Sun shines equally on both hemispheres.

Fall (September) Equinox

The Sun shines equally on both hemispheres.

3 Spring/Fall: Spring and fall begin when sunlight falls equally on both hemispheres, which happens twice a year: In March, when spring begins in the Northern Hemisphere and fall in the Southern Hemisphere; and in September, when fall begins in the Northern Hemisphere and spring in the Southern Hemisphere.

The variation in Earth's orientation relative to the Sun means that the seasons are linked to four special points in Earth's orbit:

Solstices are the two points at which sunlight becomes most extreme for the two hemispheres.

Equinoxes are the two points at which the hemispheres are equally illuminated.

Winter (December) Solstice

4 Northern Winter/Southern Summer: In December, sunlight falls less directly on the Northern Hemisphere, which makes it winter because solar energy is less concentrated and the Sun follows a shorter and lower path through the sky. The Southern Hemisphere receives more direct sunlight, making it summer.

Noon rays of sunlight hit the ground at a shallower angle in the Northern Hemisphere, meaning less concentrated sunlight and longer shadows.

Noon rays of sunlight hit the ground at a steeper angle in the Southern Hemisphere, meaning more concentrated sunlight and shorter shadows.

The Southern Hemisphere is tippedmost directly toward the Sun.

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winter begins when Earth is at the orbital point usually called the summer solstice. This apparent injustice to people in the Southern Hemisphere arose because the solstices and equi-noxes were named long ago by people living in the Northern Hemisphere. A similar injustice is inflicted on people living in equatorial regions. If you study Figure 15 carefully, you’ll see that Earth’s equator gets its most direct sunlight on the two equinoxes and its least direct sunlight on the solstices. People living near the equator therefore don’t experience four seasons in the same way as people living at mid-latitudes. Instead, equa-torial regions generally have rainy and dry seasons, with the rainy seasons coming when the Sun is higher in the sky.

In addition, seasonal variations around the times of the solstices are more extreme at high latitudes. For example, Vermont has much longer summer days and much longer winter nights than Florida. At the Arctic Circle (latitude 661

2°), the Sun remains above the horizon all day long on the summer solstice (FIGURE 18), and never rises on the winter solstice. The most extreme cases occur at the North and South Poles, where the Sun remains above the horizon for 6 months in summer and below the horizon for 6 months in winter.*

Why Orbital Distance Doesn’t Affect Our Seasons

We’ve seen that the seasons are caused by Earth’s axis tilt, not by Earth’s slightly varying distance from the Sun. Still, we might expect the varying orbital distance to play at least some role. For example, the Northern Hemisphere has winter when

Second, we usually think of the seasons in terms of weather, and the solstices and equinoxes correspond well with the beginnings of seasonal weather patterns. For example, although the Sun’s path through the Northern Hemisphere sky is long-est and highest around the time of the summer solstice, the warmest days tend to come 1 to 2 months later. To understand why, think about what happens when you heat a pot of cold soup. Even though you may have the stove turned on high from the start, it takes a while for the soup to warm up. In the same way, it takes some time for sunlight to heat the ground and oceans from the cold of winter to the warmth of summer. “Midsummer” in terms of weather therefore comes in late July and early August, which makes the summer solstice a pretty good choice for the “first day of summer.” For similar reasons, the winter solstice is a good choice for the first day of winter, and the spring and fall equinoxes are good choices for the first days of those seasons.

Seasons Around the World Notice that the names of the solstices and equinoxes reflect the northern seasons, and therefore sound backward to people who live in the Southern Hemisphere. For example, Southern Hemisphere

E

S

W

N

meridian zenith

Sun’s path onsummer (June) solstice Sun’s path

on equinoxes

Sun’s path on winter(December) solstice

FIGURE 16 This diagram shows the Sun’s path on the solstices and equinoxes for a Northern Hemisphere sky (latitude 40°N). The precise paths are different for other latitudes; for example, at latitude 40°S, the paths look similar except tilted to the north rather than to the south. Notice that the Sun rises exactly due east and sets exactly due west only on the equinoxes.

FIGURE 17 This composite photograph shows images of the Sun taken at the same time of morning (technically, at the same “mean solar time”) and from the same spot (over a large sundial in Carefree, Arizona) at 7- to 11-day intervals over the course of a year; the photo looks eastward, so north is to the left and south is to the right. Because this location is in the Northern Hemisphere, the Sun images that are high and to the north represent times near the summer solstice and the images that are low and to the south represent times near the winter solstice. The “figure 8” shape (called an analemma) arises from a combination of Earth’s axis tilt and Earth’s varying speed as it orbits the Sun.

*These statements are true for the Sun’s real position, but the bending of light by Earth’s atmosphere makes the Sun appear to be about 0.6° higher than it really is when it is near the horizon.

High Noon

When is the Sun directly overhead in your sky? Many people answer “at noon.” It’s true that the Sun reaches

its highest point each day when it crosses the meridian, giving us the term “high noon” (though the meridian crossing is rarely at precisely 12:00). However, unless you live in the Tropics (between latitudes 23.5°S and 23.5°N), the Sun is never directly overhead. In fact, any time you can see the Sun as you walk around, you can be sure it is not at your zenith. Unless you are lying down, seeing an object at the zenith requires tilting your head back into a very uncomfortable position.


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Although distance from the Sun plays no role in Earth’s seasons, the same is not true for planets that have much greater distance variations. For example, Mars has about the same axis tilt as Earth and therefore has similar seasonal patterns. However, because Mars is more than 20% closer to the Sun during its Southern Hemisphere summer than during its Northern Hemisphere summer, its Southern Hemisphere expe-riences much more extreme seasonal changes.

How does the orientation of Earth’s axis change with time?

We have now discussed both daily and seasonal changes in the sky, but there are other changes that occur over longer periods of time. One of the most important of these slow changes is precession, a gradual wobble that alters the orien-tation of Earth’s axis in space.

Precession occurs with many rotating objects. You can see it easily by spinning a top (FIGURE 20a). As the top spins rapidly, you’ll notice that its axis also sweeps out a circle at a slower rate. We say that the top’s axis precesses. Earth’s axis precesses in much the same way, but far more slowly (FIGURE 20b). Each cycle of Earth’s precession takes about 26,000 years, gradually changing where the axis points in space. Today, the axis points toward Polaris, making it our North Star. Some 13,000 years from now, Vega will be the bright star closest to true north. At most other times, the axis does not point near any bright star.

Notice that precession does not change the amount of the axis tilt (which stays close to 231

2°) and therefore does not affect the pattern of the seasons. However, because the solstices and equinoxes correspond to points in Earth’s orbit that depend on the direction the axis points in space, their positions in the orbit gradually shift with the cycle of precession. As a result, the constellations associated with the solstices and equinoxes

Earth is closer to the Sun and summer when Earth is farther away (see the lower left diagram in Figure 15), so we might expect the Northern Hemisphere to have more moderate seasons than the Southern Hemisphere. In fact, weather records show that the opposite is true: Northern Hemisphere seasons are slightly more extreme than those of the Southern Hemisphere.

The main reason for this surprising fact becomes clear when you look at a map of Earth (FIGURE 19). Most of Earth’s land lies in the Northern Hemisphere, with far more ocean in the Southern Hemisphere. As you’ll notice at any beach, lake, or pool, water takes longer to heat or cool than soil or rock (largely because sunlight heats bodies of water to a depth of many meters while heating only the very top layer of land). The water temperature therefore remains fairly steady both day and night, while the ground can heat up and cool down dramatically. The Southern Hemisphere’s larger amount of ocean moderates its climate. The Northern Hemisphere, with more land and less ocean, heats up and cools down more easily, which is why it has the more extreme seasons.

6:00 P.M.

due westNoon

due south6:00 A.M.due east

Midnightdue north

Approximate time:Direction:

FIGURE 18 This sequence of photos shows the progression of the Sun around the horizon on the summer solstice at the Arctic Circle. Notice that the Sun skims the northern horizon at midnight, then gradually rises higher, reaching its highest point when it is due South at noon.

FIGURE 19 Most land lies in the Northern Hemisphere while most ocean lies in the Southern Hemisphere. The climate-moderating effects of water make Southern Hemisphere seasons less extreme than Northern Hemisphere seasons.

equator

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and wider, and ultimately the top falls over. If there were no friction to slow its spin, the top would spin and precess forever.

The spinning (rotating) Earth precesses because of gravi-tational tugs from the Sun and Moon. Earth is not quite a perfect sphere, because it bulges at its equator. Because the equator is tilted 231

2° to the ecliptic plane, the gravitational attractions of the Sun and Moon try to pull the equatorial bulge into the ecliptic plane, effectively trying to “straighten out” Earth’s axis tilt. However, like the spinning top, Earth tends to keep rotating around the same axis. Gravity there-fore does not succeed in changing Earth’s axis tilt and instead only makes the axis precess. To gain a better understanding of precession and how it works, you might wish to experi-ment with a simple toy gyroscope. Gyroscopes are essentially

change over time. For example, a couple thousand years ago the Sun appeared in the constellation Cancer on the day of the summer solstice, but now it appears in Gemini on that day. This explains something you can see on any world map: The latitude at which the Sun is directly overhead on the summer solstice (231

2°N) is called the Tropic of Cancer, telling us that it got its name back when the Sun used to appear in Cancer on the summer solstice.

T H I N K A B O U T I TWhat constellation will the Sun be in on the summer solstice about 2000 years from now? (Hint: Figure 14 shows the names and order of the zodiac constellations.)

FIGURE 20 Precession affects the orientation of a spinning object’s axis but not the amount of its tilt.

The top spins rapidlyaround its axis . . .

. . . while its axismore slowlysweeps outa circle ofprecession. Earth rotates around its

axis every 24 hours . . .. . . while its axissweeps out a circleof precession every26,000 years.

a A spinning top wobbles, or precesses, more slowly than it spins.

b Earth’s axis also precesses. Each precession cycle takes about 26,000 years.

precession of axis

rotation rotation

Earth

’s ax

is to

day

precession of axis

Earth

’s ax

is in

A.D

. 15,

000

Polaris

Earth’s orbit

rotation rotation

Vega

Precession is caused by gravity’s effect on a tilted, rotating object that is not a perfect sphere. You have probably seen how gravity affects a top. If you try to balance a non spinning top on its point, it will fall over almost immediately. This happens because a top that is not spherical will inevitably lean a little to one side. No matter how slight this lean, gravity will quickly tip the nonspinning top over. However, if you spin the top rapidly, it does not fall over so easily. The spin-ning top stays upright because rotating objects tend to keep spinning around the same rotation axis (a consequence of the law of conservation of angular momentum). This tendency prevents gravity from immediately pulling the spinning top over, since falling over would mean a change in the spin axis from near-vertical to horizontal. Instead, gravity succeeds only in making the axis trace circles of precession. As fric-tion slows the top’s spin, the circles of precession get wider

Sun Signs

You probably know your astrological “Sun sign.” When astrology began a few thousand years ago, your Sun sign

was supposed to represent the constellation in which the Sun appeared on your birth date. However, because of precession, this is no longer the case for most people. For example, if your birthday is March 21, your Sun sign is Aries even though the Sun now appears in Pisces on that date. The problem is that astrological Sun signs are based on the positions of the Sun among the stars as they were almost 2000 years ago. Because Earth’s axis has moved about 1/13 of the way through its 26,000-year precession cycle since that time, the Sun signs are off by nearly a month from the actual positions of the Sun among the constellations today.


40


rotating wheels mounted in a way that allows them to move freely, which makes it easy to see how their spin rate affects their motion. (The fact that gyroscopes tend to keep the same rotation axis makes them very useful in aircraft and space-craft navigation.)

Phases of the Moon Tutorial, Lessons 1–3

3 THE MOON, OUR CONSTANT COMPANION

Aside from the seasons and the daily circling of the sky, the most familiar pattern of change in the sky is that of the changing phases of the Moon. We will explore these changes in this section—along with the rarer changes that occur with eclipses—and see that they are consequences of the Moon’s orbit around Earth.

Why do we see phases of the Moon?

As the Moon orbits Earth, it returns to the same position relative to the Sun in our sky (such as along the Earth-Sun line) about every 29 12 days. This time period marks the cycle of lunar phases, in which the Moon’s appearance in our sky changes as its position relative to the Sun changes. This 29 12-day period is also the origin of the word month (think “moonth”).

The Moon’s Orbit to Scale FIGURE 21 shows the Moon’s orbit on a 1-to-10-billion scale model of the so-lar system. On this scale, the Sun is about the size of a large grapefruit, which means the entire orbit of the Moon could fit inside it. When you then consider the fact that the Sun is located 15 meters away on this scale, you’ll realize that for practical purposes the Sun’s rays all hit Earth and the Moon from the same direction. This fact is helpful to understanding the Moon’s phases, because it means we can think of sunlight coming from a single direction at both Earth and the Moon, an effect shown clearly in the inset photo. The figure also shows the elliptical shape of the Moon’s orbit, which causes the Earth-Moon distance to vary between about 356,000 and 407,000 kilometers.

FIGURE 21 The Moon’s orbit on a 1-to-10-billion scale; black labels indicate the Moon’s actual distance at its nearest to and farthest from Earth. The orbit is so small compared to the distance to the Sun that sunlight strikes the entire orbit from the same direc-tion. You can see this in the inset photo, which shows the Moon and Earth photographed from Mars by the Mars Reconnaissance Orbiter.

Earth at oneten-billionthof actual size.

The Moon and its orbitat one ten-billionth ofactual size.

Sunlight

356,000 km 407,000 km

Orbit of Earth/M

oon around Sun

The Sun is 15 meters awayon this scale, so sunlightcomes from essentially thesame direction all along theMoon’s orbit.

S E E I T F O R YO U R S E L FLike the Sun, the Moon appears to move gradually eastward through the constellations of the zodiac. However, while the Sun takes a year for each circuit, the Moon takes only about a month, which means it moves at a rate of about 360° per month, or 1

2°—its own angular size—each hour. If the Moon is visible tonight, go out and note its location relative to a few bright stars. Then go out again a couple hours later. Can you notice the Moon’s change in position relative to the stars?

Understanding Phases The easiest way to understand the lunar phases is with the simple demonstration illustrated in FIGURE 22. Take a ball outside on a sunny day. (If it’s dark

or cloudy, you can use a flashlight instead of the Sun; put the flashlight on a table a few meters away and shine it toward you.) Hold the ball at arm’s length to represent the Moon while your head represents Earth. Slowly spin counterclockwise so that the ball goes around you the way the Moon orbits Earth. (If you live in the Southern Hemisphere, spin clockwise because you view the sky “upside down” compared to the Northern Hemisphere.) As you turn, you’ll see the ball go through phases just like the Moon’s. If you think about what’s happening, you’ll realize that the phases of the ball result from just two basic facts:

1. Half the ball always faces the Sun (or flashlight) and therefore is bright, while the other half faces away from the Sun and therefore is dark.

2. As you look at the ball at different positions in its “orbit” around your head, you see different combinations of its bright and dark faces.

For example, when you hold the ball directly opposite the Sun, you see only the bright portion of the ball, which represents the “full” phase. When you hold the ball at its “first-quarter” posi-tion, half the face you see is dark and the other half is bright.

We see lunar phases for the same reason. Half the Moon is always illuminated by the Sun, but the amount of this illu-minated half that we see from Earth depends on the Moon’s position in its orbit. The photographs in Figure 22 show how the phases look.

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are waning, or “decreasing.” Also notice that no phase is called a “half moon.” Instead, we see half the Moon’s face at first-quarter and third-quarter phases; these phases mark the times when the Moon is one quarter or three quarters of the way through its monthly cycle (which begins at new moon). The phases just before and after new moon are called crescent, while those just before and after full moon are called gibbous (pronounced with a hard g as in “gift”). A gibbous moon is

The Moon’s phase is directly related to the time it rises, reaches its highest point in the sky, and sets. For example, the full moon must rise around sunset, because it occurs when the Moon is opposite the Sun in the sky. It therefore reaches its highest point in the sky at midnight and sets around sunrise. Similarly, a first-quarter moon must rise around noon, reach its highest point around 6 p.m., and set around midnight, because it occurs when the Moon is about 90° east of the Sun in our sky. Figure 22 lists the approximate rise, highest point, and set times for each phase.

New MoonRise: 6 A.M.

Highest: noonSet: 6 P.M.

Waxing CrescentRise: 9 A.M.

Highest: 3 P.M.

Set: 9 P.M.

First QuarterRise: noon

Highest: 6 P.M.

Set: midnight

To Sun

Waxing GibbousRise: 3 P.M.

Highest: 9 P.M.

Set: 3 A.M.

Full MoonRise: 6 P.M.

Highest: midnightSet: 6 A.M.

Waning GibbousRise: 9 P.M.

Highest: 3 A.M.

Set: 9 A.M.

Third QuarterRise: midnightHighest: 6 A.M.

Set: noon

Waning CrescentRise: 3 A.M.

Highest: 9 A.M.

Set: 3 P.M.

. . . but what you see varies. If you turn to look at the ball (Moon) here, for example,you see only the bright half, so it appears full.

Rise, high point, and set times areapproximate. Exact times depend on your location, the time of year,and details of the Moon’s orbit.

Photos show phases as they appear in theNorthern Hemisphere; turn the book upsidedown to see how the same phases appearfrom the Southern Hemisphere.

Notice that half the ball (Moon)always faces the Sun and is bright,while the other half is dark . . .

FIGURE 22 A simple demonstration illustrates the phases of the Moon. The half of the ball (Moon) facing the Sun is always illuminated while the half facing away is always dark, but you see the ball go through phases as it orbits around your head (Earth). (The new moon photo shows blue sky, because a new moon is always close to the Sun in the sky and hence hidden from view by the bright light of the Sun.)

T H I N K A B O U T I TSuppose you go outside in the morning and notice that the visible face of the Moon is half light and half dark. Is this a first-quarter or third-quarter moon? How do you know?

Shadows and the Moon

Many people guess that the Moon’s phases are caused by Earth’s shadow falling on its surface, but this is not

the case. As we’ve seen, the Moon’s phases are caused by the fact that we see different portions of its day and night sides at different times as it orbits around Earth. The only time Earth’s shadow falls on the Moon is during the relatively rare event of a lunar eclipse.


Notice that the phases from new to full are said to be waxing, which means “increasing.” Phases from full to new

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essentially the opposite of a crescent moon—a crescent moon has a small sliver of light while a gibbous moon has a small sliver of dark. The term gibbous literally means “hump-backed,” so you can see how the gibbous moon got its name.

The Moon’s Synchronous Rotation Although we see many phases of the Moon, we do not see many faces. From Earth we always see (nearly*) the same face of the Moon. This happens because the Moon rotates on its axis in the same amount of time it takes to orbit Earth, a trait called synchro-nous rotation. A simple demonstration shows the idea. Place a ball on a table to represent Earth while you represent the Moon. Start by facing the ball. If you do not rotate as you walk around the ball, you’ll be looking away from it by the time you are halfway around your orbit (FIGURE 23a). The only way you can face the ball at all times is by completing exactly one rotation while you complete one orbit (FIGURE 23b). Note that the Moon’s synchronous rotation is not a coincidence; rather, it is a consequence of Earth’s gravity affecting the Moon in much the same way the Moon’s gravity causes tides on Earth.

The View from the Moon A good way to solidify your understanding of the lunar phases is to imagine that you live on the side of the Moon that faces Earth. For example, what would you see if you looked at Earth when people on Earth saw a new moon? By remembering that a new moon occurs when the Moon is between the Sun and Earth, you’ll realize that from the Moon you’d be looking at Earth’s day-time side and hence would see a full earth. Similarly, at full moon you would be facing the night side of Earth and would see a new earth. In general, you’d always see Earth in a phase opposite the phase of the Moon seen by people on

a If you do not rotate while walking around the model, you will not always face it.

b You will face the model at all times only if you rotate exactly once during each orbit.

FIGURE 23 The fact that we always see the same face of the Moon means that the Moon must rotate once in the same amount of time it takes to orbit Earth once. You can see why by walking around a model of Earth while imagining that you are the Moon.

*Because the Moon’s orbital speed varies (in accord with Kepler’s second law) while its rotation rate is steady, the visible face appears to wobble slightly back and forth as the Moon orbits Earth. This effect, called libration, allows us to see a total of about 59% of the Moon’s surface over the course of a month, even though we see only 50% of the Moon at any single time.

Earth at the same time. Moreover, because the Moon always shows nearly the same face to Earth, Earth would appear to hang nearly stationary in your sky as it went through its cycle of phases.

T H I N K A B O U T I TAbout how long would each day and night last if you lived on the Moon? Explain.

Thinking about the view from the Moon clarifies another interesting feature of the lunar phases: The dark portion of the lunar face is not totally dark. Just as we can see at night by the light of the Moon, if you were in the dark area of the Moon during crescent phase your moonscape would be illuminated by a nearly full (gibbous) Earth. In fact, because Earth is much larger than the Moon, the illumination would be much greater than what the full moon provides on Earth. In other words, sunlight reflected by Earth faintly illuminates the “dark” portion of the Moon’s face. We call this illumination the ashen light, or earthshine, and it enables us to see the outline of the full face of the Moon even when the Moon is not full.

The “Dark Side” of the Moon

Some people refer to the far side of the Moon—meaning the side that we never see from Earth—as the dark side.

But this is not correct, because the far side is not always dark. For example, during new moon the far side faces the Sun and hence is completely sunlit. In fact, because the Moon rotates with a period of approximately one month (the same time it takes to orbit Earth), points on both the near and the far side have two weeks of daylight alternating with two weeks of dark-ness. The only time the far side is completely dark is at full moon, when it faces away from both the Sun and Earth.


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plane (the plane of Earth’s orbit around the Sun). To visualize this inclination, imagine the ecliptic plane as the surface of a pond, as shown in FIGURE 24. Because of the inclination of its orbit, the Moon spends most of its time either above or below this surface. It crosses through this surface only twice during each orbit: once coming out and once going back in. The two points in each orbit at which the Moon crosses the surface are called the nodes of the Moon’s orbit.

Notice that the nodes are aligned approximately the same way (diagonally on the page in Figure 24) throughout the year, which means they lie along a nearly straight line with

Eclipses Tutorial, Lessons 1–3

What causes eclipses?

Occasionally, the Moon’s orbit around Earth causes events much more dramatic than lunar phases. The Moon and Earth both cast shadows in sunlight, and these shadows can create eclipses when the Sun, Earth, and Moon fall into a straight line. Eclipses come in two basic types:

■ A lunar eclipse occurs when Earth lies directly between the Sun and Moon, so Earth’s shadow falls on the Moon.

■ A solar eclipse occurs when the Moon lies directly between the Sun and Earth, so the Moon’s shadow falls on Earth.

Note that, because Earth is much larger than the Moon, Earth’s shadow can cover the entire Moon during a lunar eclipse. Therefore, a lunar eclipse can be seen by anyone on the night side of Earth when it occurs. In contrast, the Moon’s shadow can cover only a small portion of Earth at any one moment, so you must be living within the relatively small pathway through which the shadow moves to see a solar eclipse. That is why you see lunar eclipses more often than solar eclipses, even though both types occur about equally often.

Conditions for Eclipses Look once more at Figure 22. The figure makes it look as if the Sun, Earth, and Moon line up with every new and full moon. If this figure told the whole story of the Moon’s orbit, we would have both a lunar and a solar eclipse every month—but we don’t.

The missing piece of the story in Figure 22 is that the Moon’s orbit is slightly inclined (by about 5°) to the ecliptic

Moon in the Daytime and Stars

on the Moon

Night is so closely associated with the Moon in traditions and stories that many people mistakenly believe that the

Moon is visible only in the nighttime sky. In fact, the Moon is above the horizon as often in the daytime as at night, though it is easily visible only when its light is not drowned out by sunlight. For example, a first-quarter moon is easy to spot in the late afternoon as it rises through the eastern sky, and a third-quarter moon is visible in the morning as it heads toward the western horizon.

Another misconception appears in illustrations that show a star in the dark portion of the crescent moon. The star in the dark portion appears to be in front of the Moon, which is impossible because the Moon is much closer to us than is any star.


Nodes are the points where the Moon’sorbit crosses the ecliptic plane.

The pond surface represents the ecliptic plane (the plane of Earth’s orbit around the Sun); not to scale!

Full moon near node:lunar eclipse

Full moon near node:lunar eclipse

New moon near node:solar eclipse

New moon near node:solar eclipse

Full moon above ecliptic plane:no eclipse

New moon belowecliptic plane: no eclipse

Full moon below ecliptic plane:no eclipse

New moon above ecliptic plane:no eclipse

FIGURE 24 This illustration represents the ecliptic plane as the surface of a pond. The Moon’s orbit is tilted by about 5° to the ecliptic plane, so the Moon spends half of each orbit above the plane (the pond surface) and half below it. Eclipses occur only when the Moon is at both a node (passing through the pond surface) and a phase of either new moon (for a solar eclipse) or full moon (for a lunar eclipse)—as is the case with the lower left and top right orbits shown.

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Moon passes through Earth’s umbra and we see a total lunar eclipse. If the alignment is somewhat less perfect, only part of the full moon passes through the umbra (with the rest in the penumbra) and we see a partial lunar eclipse. If the Moon passes through only Earth’s penumbra, we see a penumbral lunar eclipse. Penumbral eclipses are the most common type of lunar eclipse, but they are the least visually impressive because the full moon darkens only slightly.

Total lunar eclipses are the most spectacular. The Moon becomes dark and eerily red during totality, when the Moon is entirely engulfed in the umbra. Totality usually lasts about an hour, with partial phases both before and after. The curva-ture of Earth’s shadow during partial phases shows that Earth is round (FIGURE 27). To understand the redness during total-ity, consider the view of an observer on the eclipsed Moon, who would see Earth’s night side surrounded by the reddish glow of all the sunrises and sunsets occurring on the Earth at that moment. It is this reddish light that illuminates the Moon during total eclipse.

Solar Eclipses We can also see three types of solar eclipse (FIGURE 28). If a solar eclipse occurs when the Moon is in a part of its orbit where it is relatively close to Earth (see Fig-ure 21), the Moon’s umbra can cover a small area of Earth’s surface (up to about 270 kilometers in diameter). Within this area you will see a total solar eclipse. If the eclipse oc-curs when the Moon is in a part of its orbit that puts it far-ther from Earth, the umbra may not reach Earth’s surface at all. In that case, you will see an annular eclipse—a ring of sunlight surrounding the Moon—in the small region of Earth directly behind the umbra. In either case, the region of totality or annularity will be surrounded by a much larger region (typically about 7000 kilometers in diameter) that falls within the Moon’s penumbral shadow. Here you will see a partial solar eclipse, in which only part of the Sun is blocked from view. The combination of Earth’s rotation and the Moon’s orbital motion causes the Moon’s shadows to race across the

penumbra

umbra

FIGURE 25 The shadow cast by an object in sunlight. Sunlight is fully blocked in the umbra and partially blocked in the penumbra.

FIGURE 27 This multiple-exposure photograph shows the progres-sion (left to right) of a total lunar eclipse observed from Tenerife, Canary Islands (Spain). Totality began (far right) just before the Moon set in the west. Notice Earth’s curved shadow advancing across the Moon during the partial phases, and the redness of the full moon during totality.

Penumbral Lunar Eclipse

Moon passes through penumbra.

Partial Lunar Eclipse

Part of the Moon passes through umbra.

Total Lunar Eclipse

Moon passes entirely through umbra.

FIGURE 26 The three types of lunar eclipse.

the Sun and Earth about twice each year. We therefore find the following conditions for an eclipse to occur:

1. The phase of the Moon must be full (for a lunar eclipse) or new (for a solar eclipse).

2. The new or full moon must occur during one of the periods when the nodes of the Moon’s orbit are aligned with the Sun and Earth.

Inner and Outer Shadows Figure 24 shows the Moon and Earth each casting only a simple “shadow cone” (extend-ing away from the Sun) at each position shown. However, a closer look at the geometry shows that the shadow of the Moon or Earth actually consists of two distinct regions: a cen-tral umbra, where sunlight is completely blocked, and a sur-rounding penumbra, where sunlight is only partially blocked (FIGURE 25). The shadow cones in Figure 24 represent only the umbra, but both shadow regions are important to under-standing eclipses.

Lunar Eclipses A lunar eclipse begins at the moment when the Moon’s orbit first carries it into Earth’s penumbra. After that, we will see one of three types of lunar eclipse (FIGURE 26). If the Sun, Earth, and Moon are nearly perfectly aligned, the


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and planets and bright stars become visible in the daytime. As totality ends, the Sun slowly emerges from behind the Moon over the next couple of hours. However, because your eyes have adapted to the darkness, totality appears to end far more abruptly than it began.

Predicting Eclipses Few phenomena have so inspired and humbled humans throughout the ages as eclipses. For many cultures, eclipses were mystical events associated with fate or the gods, and countless stories and legends surround them. One legend holds that the Greek philosopher Thales (c. 624–546 b.c.) successfully predicted the year (but presum-ably not the precise time) that a total eclipse of the Sun would be visible in the area where he lived, which is now part of Turkey. The eclipse occurred as two opposing armies (the Medes and the Lydians) were massing for battle, and it so frightened them that they put down their weapons, signed a treaty, and returned home. Because modern research shows that the only eclipse vis-ible in that part of the world at about that time occurred on May 28, 585 b.c., we know the precise date on which the treaty was signed—the earliest historical event that can be dated precisely.

Much of the mystery of eclipses probably stems from the relative difficulty of predicting them. Look again at Figure 24. The two periods each year when the nodes of the Moon’s orbit are nearly aligned with the Sun are called eclipse seasons. Each eclipse season lasts a few weeks. Some type of lunar eclipse occurs during each eclipse season’s full moon, and some type of solar eclipse occurs during its new moon.

If Figure 24 told the whole story, eclipse seasons would occur every 6 months and predicting eclipses would be easy. For example, if eclipse seasons always occurred in January and July, eclipses would always occur on the dates of new and full moons in those months. Actual eclipse prediction is

face of Earth at a typical speed of about 1700 kilometers per hour. As a result, the umbral shadow traces a narrow path across Earth, and totality never lasts more than a few minutes in any particular place.

A total solar eclipse is a spectacular sight. It begins when the disk of the Moon first appears to touch the Sun. Over the next couple of hours, the Moon appears to take a larger and larger “bite” out of the Sun. As totality approaches, the sky darkens and temperatures fall. Birds head back to their nests, and crickets begin their nighttime chirping. During the few minutes of totality, the Moon completely blocks the normally visible disk of the Sun, allowing the faint corona to be seen (FIGURE 29). The surrounding sky takes on a twilight glow,

b This photo from Earth orbit shows the Moon‘s shadow (umbra) on Earth during a total solar elipse. Notice that only a small region of Earth experiences totality at any one time.

a The three types of solar eclipse. The diagrams show the Moon‘s shadow falling on Earth; note the dark central umbra surrounded by the much lighter penumbra.

path oftotal eclipse

path ofannular eclipse

Moon

Moon

A total solar eclipse occurs in the small central region.

If the Moon’s umbral shadow does not reach Earth, an annular eclipse occurs in the small central region.

A partial solar eclipse occurs in the lighter area surrounding the area of totality.

Total SolarEclipse

Partial SolarEclipse

Annular SolarEclipse

FIGURE 28 During a solar eclipse, the Moon’s small shadow moves rapidly across the face of Earth.

FIGURE 29 This multiple-exposure photograph shows the progres-sion of a total solar eclipse over La Paz, Mexico. Totality (central image) lasts only a few minutes, during which time we can see the faint corona around the outline of the Sun. The foreground church was photographed at a different time of day.

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more difficult than this because of something the figure does not show: The nodes slowly move around the Moon’s orbit, so the eclipse seasons occur slightly less than 6 months apart (about 173 days apart).

The combination of the changing dates of eclipse seasons and the 291

2-day cycle of lunar phases makes eclipses recur in a cycle of about 18 years, 111

3 days, called the saros cycle. Astronomers in many ancient cultures identified the saros cycle and used it to make eclipse predictions. For example, in the Middle East the Babylonians achieved remarkable success at predicting eclipses more than 2500 years ago, and the Mayans achieved similar success in Central America; in fact, the Mayan calendar includes a cycle (the sacred round) of 260 days—almost exactly 11

2 times the 173.32 days between successive eclipse seasons.

TABLE 1 Lunar Eclipses 2013–2016*Date Type Where You Can See It

April 25, 2013

partial Europe, Africa, Asia, Australia

May 25, 2013

penumbral Americas, Africa

Oct. 18, 2013

penumbral Americas, Europe, Africa, Asia

April 15, 2014

total Australia, Pacific, Americas

Oct. 8, 2014

total Asia, Australia, Pacific, Americas

April 4, 2015

total Asia, Australia, Pacific, Americas

Sept. 28, 2015

total Americas, Europe, Africa

March 23, 2016

penumbral Asia, Australia, Pacific, western Americas

Sept. 16, 2016

penumbral Europe, Africa, Asia, Australia

*Dates are based on Universal Time and hence are those in Greenwich, England, at the time of the eclipse; check a news source for the local time and date. Eclipse predictions by Fred Espenak, NASA GSFC.

T H I N K A B O U T I TIn Table 1, notice that there’s one exception to the “rule” of eclipses coming a little less than 6 months apart: the 2013 lunar eclipses of April 25 and May 25. How can eclipses occur just a month apart? Explain.

S P E C I A L TO P I CDoes the Moon Influence Human Behavior?

From myths of werewolves to stories of romance under the full moon, human culture is filled with claims that the Moon influences our behavior. Can we say anything scientific about such claims?

The Moon clearly has important influences on Earth, perhaps most notably through its role in creating tides. Although the Moon’s tidal force cannot directly affect objects as small as people, the ocean tides have indirect effects. For example, fishermen, boaters, and surf-ers all adjust at least some of their activities to the cycle of the tides.

Another potential influence might come from the lunar phases. Physiological patterns in many species appear to follow the lunar phases; for example, some crabs and turtles lay eggs only at full moon. No human trait is so closely linked to lunar phases, but the average

human menstrual cycle is so close in length to a lunar month that it is difficult to believe the similarity is mere coincidence.

Nevertheless, aside from the physiological cycles and the influ-ence of tides on people who live near the oceans, claims that the lunar phase affects human behavior are difficult to verify scientifi-cally. For example, although it is possible that the full moon brings out certain behaviors, it may also simply be that some behaviors are easier to engage in when the sky is bright. A beautiful full moon may bring out your desire to walk on the beach under the moonlight, but there is no scientific evidence to suggest that the full moon would affect you the same way if you were confined to a deep cave.

However, while the saros cycle allows you to predict when an eclipse will occur, it does not allow you to predict exactly where or the precise type of eclipse. For example, if a total solar eclipse occurred today, another would occur 18 years 111

3 days from now, but it would not be visible from the same places on Earth and might be annular or partial rather than total. No ancient culture achieved the ability to predict eclipses in every detail.

Today, we can predict eclipses because we know the precise details of the orbits of Earth and the Moon. TABLE 1 lists upcoming lunar eclipses; notice that, as we expect, eclipses generally come a little less than 6 months apart. FIGURE 30 shows paths of totality for upcoming total solar eclipses (but not for partial or annular eclipses), using color coding to show eclipses that repeat with the saros cycle.

2031 Nov. 14

2021 Dec. 04

2026

Aug

. 12

2024

Apr.

08

2015 M

ar. 2

0

2017 Aug. 21

2033 Mar. 30

2020 Dec. 14

2013 Nov. 03

2016 Mar. 09 2027 Aug. 02

2019 Jul. 02

2016 Mar. 09

2030 Nov. 25 2028 Jul. 22

2037 Jul. 13

2034 Mar. 202035 Sep. 02

FIGURE 30 This map shows the paths of totality for solar eclipses from 2013 through 2037. Paths of the same color represent eclipses occurring in successive saros cycles, separated by 18 years 11 days. For example, the 2034 eclipse occurs 18 years 11 days after the 2016 eclipse (both shown in red). Eclipse predictions by Fred Espenak, NASA GSFC.

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4 THE ANCIENT MYSTERY OF THE PLANETS

We’ve now covered the appearance and motion of the stars, Sun, and Moon in the sky. That leaves us with the planets yet to discuss. As you’ll soon see, planetary motion posed an ancient mystery that played a critical role in the development of modern civilization.

Five planets are easy to find with the naked eye: Mercury, Venus, Mars, Jupiter, and Saturn. Mercury is visible infre-quently, and only just after sunset or just before sunrise because it is so close to the Sun. Venus often shines brightly in the early evening in the west or before dawn in the east. If you see a very bright “star” in the early evening or early morning, it is prob-ably Venus. Jupiter, when it is visible at night, is the brightest object in the sky besides the Moon and Venus. Mars is often recognizable by its reddish color, though you should check a star chart to make sure you aren’t looking at a bright red star. Saturn is also easy to see with the naked eye, but because many stars are just as bright as Saturn, it helps to know where to look. (It also helps to know that planets tend not to twinkle as much as stars.) Sometimes several planets may appear close together in the sky, offering a particularly beautiful sight (FIGURE 31).

S E E I T F O R YO U R S E L FUsing astronomical software or the Web, find out what planets are visible tonight and where to look for them, then go out and try to find them. Are they easy or difficult to identify?

Jupiter

Saturn

Mars

Venus

Mercury

Saturn

Mars

Venus

Jupiter

Mercury

FIGURE 31 This photograph shows a grouping in our sky of all five planets that are easily visible to the naked eye. It was taken near Chatsworth, New Jersey, on April 23, 2002. The next such close grouping of these five planets in our sky will occur in September 2040.

Aug. 27

Sept. 29

July 30

East West

November

June

Mars usually moves eastwardrelative to the stars . . .

. . . but it reversescourse during its apparent retrograde motion.

FIGURE 32 This composite of 29 individual photos (taken at 5- to 8-day intervals in 2003) shows a retrograde loop of Mars. Note that Mars is biggest and brightest in the middle of the retrograde loop, because that is where it is closest to Earth in its orbit. (The faint dots just right of center are images of the planet Uranus, which by coincidence was in the same part of the sky.)

Why was planetary motion so hard to explain?

Over the course of a single night, planets behave like all other objects in the sky: Earth’s rotation makes them appear to rise in the east and set in the west. But if you continue to watch the planets night after night, you will notice that their movements among the constellations are quite complex. Instead of moving steadily eastward relative to the stars, like the Sun and Moon, the planets vary substantially in both speed and brightness; in fact, the word planet comes from the Greek for “wandering star.” Moreover, while the planets usually move eastward through the constellations, they occasionally reverse course, moving westward through the zodiac (FIGURE 32). These periods of apparent retrograde motion (retrograde means “backward”) last from a few weeks to a few months, depending on the planet.

For ancient people who believed in an Earth-centered universe, apparent retrograde motion was very difficult to explain; after all, what could make planets sometimes turn around and go backward if everything moves in circles around Earth? The ancient Greeks came up with some very clever ways to explain it, but their explanations were quite complex.

In contrast, apparent retrograde motion has a simple explanation in a Sun-centered solar system. You can demon-strate it for yourself with the help of a friend (FIGURE 33a). Pick a spot in an open area to represent the Sun. You can represent Earth by walking counterclockwise around the Sun, while your friend represents a more distant planet (such as Mars or Jupiter) by walking in the same direction around the Sun at a greater distance. Your friend should walk more slowly than you, because more distant planets orbit the Sun more slowly. As you walk, watch how your friend appears to

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76 5 4 3

217

6 5 4 32

1

Mars orbit

Follow the lines of sight from inner person(planet) to outer person (planet) to seewhere the outer one appears againstthe background.

a The retrograde motion demonstration: Watch how your friend (in red) usually appears to move forward against the background of the building in the distance but appears to move backward as you (in blue) catch up to and pass her in your “orbit.”

b This diagram shows how the same idea applies to a planet. Follow the lines of sight from Earth to Mars in numerical order. Notice that Mars appears to move westward relative to the distant stars as Earth passes it by in its orbit (roughly from points 3 to 5).

Earth orbit

Leo

Cancer

Gemini

Eas

t West

Apparent retrograde motion occursbetween positions 3 and 5, as theinner person (planet) passes theouter person (planet).

7

65

43 2

1

7

65

43

21

FIGURE 33 Apparent retrograde motion—the occasional “backward” motion of the planets relative to the stars—has a simple explanation in a Sun-centered solar system.

move relative to buildings or trees in the distance. Although both of you always walk the same way around the Sun, your friend will appear to move backward against the background during the part of your “orbit” in which you catch up to and pass him or her. FIGURE 33b shows how the same idea applies to Mars. Note that Mars never actually changes direction; it only appears to go backward as Earth passes Mars in its orbit. (To understand the apparent retrograde motions of Mercury and Venus, which are closer to the Sun than is Earth, simply switch places with your friend and repeat the demonstration.)

Why did the ancient Greeks reject the real explanation for planetary motion?

If the apparent retrograde motion of the planets is so read-ily explained by recognizing that Earth orbits the Sun, why wasn’t this idea accepted in ancient times? In fact, the idea that Earth goes around the Sun was suggested as early as 260 b.c. by the Greek astronomer Aristarchus (see Special Topic). Nevertheless, Aristarchus’s contemporaries rejected his idea, and the Sun-centered solar system did not gain wide accept-ance until almost 2000 years later.

Although there were many reasons the Greeks were reluc-tant to abandon the idea of an Earth-centered universe, one of the most important was their inability to detect what we call stellar parallax. Extend your arm and hold up one finger. If you keep your finger still and alternately close your left eye and right eye, your finger will appear to jump back and forth against the background. This apparent shifting, called parallax, occurs because your two eyes view your finger from opposite sides of your nose. If you move your finger closer to your face, the parallax increases. If you look at a distant tree or

flagpole instead of your finger, you may not notice any parallax at all. In other words, parallax depends on distance, with nearer objects exhibiting greater parallax than more distant objects.

If you now imagine that your two eyes represent Earth at opposite sides of its orbit around the Sun and that the tip of your finger represents a relatively nearby star, you have the idea of stellar parallax. That is, because we view the stars from different places in our orbit at different times of year, nearby stars should appear to shift back and forth against the back-ground of more distant stars (FIGURE 34).

FIGURE 34 Stellar parallax is an apparent shift in the position of a nearby star as we look at it from different places in Earth’s orbit. This figure is greatly exaggerated; in reality, the amount of shift is far too small to detect with the naked eye.

July

nearby star

distant stars

January

Every January,we see this:

Every July,we see this:

As Earthorbits theSun . . .

. . . the position of a nearbystar appears to shift againstthe background of moredistant stars.

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T H I N K A B O U T I THow far apart are opposite sides of Earth’s orbit? How far away are the nearest stars? Using the 1-to-10-billion scale, describe the challenge of detecting stellar parallax.

S P E C I A L TO P I CWho First Proposed a Sun-Centered Solar System?

You’ve probably heard of Copernicus, whose work in the 16th century started the revolution that ultimately overturned the ancient belief in an Earth-centered universe. However, the idea that Earth goes around the Sun was proposed much earlier by the Greek scientist Aristarchus (c. 310–230 b.c.).

Little of Aristarchus’s work survives to the present day, so we cannot know what motivated him to suggest an idea so contrary to the prevailing view of an Earth-centered universe. However, it’s likely that he was motivated by the fact that a Sun-centered system offers a much more natural explanation for the apparent retro-grade motion of the planets. To account for the lack of detectable stellar parallax, Aristarchus suggested that the stars were extremely far away.

Aristarchus further strengthened his argument by estimating the sizes of the Moon and the Sun. By observing the shadow of Earth on the Moon during a lunar eclipse, he estimated the Moon’s diam-eter to be about one-third of Earth’s diameter—only slightly more than the actual value. He then used a geometric argument, based on measuring the angle between the Moon and the Sun at first- and third-quarter phases, to conclude that the Sun must be larger than

Earth. (Aristarchus’s measurements were imprecise, so he estimated the Sun’s diameter to be about 7 times Earth’s rather than the correct value of about 100 times.) His conclusion that the Sun is larger than Earth may have been another reason he believed that Earth should orbit the Sun, rather than vice versa.

Although Aristarchus was probably the first to suggest that Earth orbits the Sun, his ideas built on the work of earlier scholars. For example, Heracleides (c. 388–315 b.c.) had previously suggested that Earth rotates, which offered Aristarchus a way to explain the daily circling of the sky in a Sun-centered system. Heracleides also suggested that not all heavenly bodies circle Earth: Based on the fact that Mercury and Venus always stay fairly close to the Sun in the sky, he argued that these two planets must orbit the Sun. In suggest-ing that all the planets orbit the Sun, Aristarchus was extending the ideas of Heracleides and others before him.

Aristarchus gained little support among his contemporaries, but his ideas never died, and Copernicus was aware of them when he proposed his own version of the Sun-centered system. Thus, our modern understanding of the universe owes at least some debt to the remarkable vision of a man born more than 2300 years ago.

The Big Picture

Putting This Chapter into Context

In this chapter, we surveyed the phenomena of our sky. Keep the following “big picture” ideas in mind as you continue your study of astronomy:

■ You can enhance your enjoyment of astronomy by observing the sky. The more you learn about the appearance and apparent motions of the sky, the more you will appreciate what you can see in the universe.

■ From our vantage point on Earth, it is convenient to imagine that we are at the center of a great celestial sphere—even though

we really are on a planet orbiting a star in a vast universe. We can then understand what we see in the local sky by thinking about how the celestial sphere appears from our latitude.

■ Most of the phenomena of the sky are relatively easy to observe and understand. The more complex phenomena—particularly eclipses and apparent retrograde motion of the planets—challenged our ancestors for thousands of years. The desire to understand these phenomena helped drive the development of science and technology.

Because the Greeks believed that all stars lie on the same celestial sphere, they expected to see stellar parallax in a slightly different way. If Earth orbited the Sun, they reasoned, at different times of year we would be closer to different parts of the celestial sphere and would notice changes in the angu-lar separation of stars. However, no matter how hard they searched, they could find no sign of stellar parallax. They concluded that one of the following must be true:

1. Earth orbits the Sun, but the stars are so far away that stellar parallax is undetectable to the naked eye.

2. There is no stellar parallax because Earth remains stationary at the center of the universe.

Aside from a few notable exceptions such as Aristarchus, the Greeks rejected the correct answer (the first one) because they could not imagine that the stars could be that far away.

Today, we can detect stellar parallax with the aid of telescopes, providing direct proof that Earth really does orbit the Sun. Careful measurements of stellar parallax also provide the most reliable means of measuring distances to nearby stars.

The ancient mystery of the planets drove much of the historical debate over Earth’s place in the universe. In many ways, the modern technological society we take for granted today can be traced directly to the scientific revolution that began in the quest to explain the strange wanderings of the planets among the stars in our sky.

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